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## Re: [ontolog-forum] Universal Basic Semantic Structures

 To: ontolog-forum@xxxxxxxxxxxxxxxx John F Sowa Sun, 30 Sep 2012 13:10:25 -0400 <50687D01.9030106@xxxxxxxxxxx>
 ```On 9/30/2012 10:04 AM, Chris Menzel wrote: > Set theory didn't exist in any systematic form before Cantor and sets > /per se/ weren't objects of mathematical interest; at most they showed > up in the analysis of logic, as you note in the cases of Boole and Peirce.    (01) I dusted off my copy of Boole (1854), and it is rather impressive. He did not use the word 'set', but he distinguished three terms:    (02) 1. Propositions -- which can have truth values 1 or 0, but he also discussed the use of values between 0 and 1 for probabilities.    (03) 2. Classes -- which correspond to sets, but without the option of considering classes of classes.    (04) 3. Class terms -- which correspond to the monadic predicates used in syllogisms.    (05) I agree that what is currently called 'set theory' did not exist before Cantor. But Boole's treatment is remarkably systematic for such an early development.    (06) Many applications of what people call 'sets' don't use anything that goes beyond Boolean classes or collections. In fact, John Venn invented his diagrams to illustrate Boolean operations and their relationship to syllogisms.    (07) Most people (and most programmers) who use the word 'set' think in terms of Venn diagrams, and they never use sets of sets.    (08) JFS > But pedagogically, it helps to start with Boolean algebra and show > how many other theories can be developed as specializations of it.    (09) CM > I'm not at all sure that's the best way to study set theory; indeed, > I fear it encourages the confusion between the two conceptions > of set noted above.    (010) To avoid confusion, I would reserve the word 'set' for Cantor's version. But teaching people Boolean algebra is useful for many purposes:    (011) 1. It shows the underlying commonalities in the operations on propositions, predicates, and collections.    (012) 2. It provides a useful theory of collections that programmers and linguists often use, but mistakenly identify with set theory.    (013) 3. It clarifies the relationships between set theory and mereology.    (014) As you know, I believe that looking at the lattice of all possible theories that use a given logic helps clarify seemingly unrelated issues. The example of Boolean algebra illustrates that point.    (015) John    (016) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (017) ```
 Current Thread Re: [ontolog-forum] Universal Basic Semantic Structures, (continued) Re: [ontolog-forum] Universal Basic Semantic Structures, William Frank Re: [ontolog-forum] Universal Basic Semantic Structures, doug foxvog Re: [ontolog-forum] Universal Basic Semantic Structures, William Frank Re: [ontolog-forum] Universal Basic Semantic Structures, John F Sowa Re: [ontolog-forum] Universal Basic Semantic Structures, William Frank Re: [ontolog-forum] Universal Basic Semantic Structures, Avril Styrman Re: [ontolog-forum] Universal Basic Semantic Structures, Chris Menzel Re: [ontolog-forum] Universal Basic Semantic Structures, Matthew West Re: [ontolog-forum] Universal Basic Semantic Structures, John F Sowa Re: [ontolog-forum] Universal Basic Semantic Structures, Chris Menzel Re: [ontolog-forum] Universal Basic Semantic Structures, John F Sowa <= Re: [ontolog-forum] Universal Basic Semantic Structures, Avril Styrman Re: [ontolog-forum] Universal Basic Semantic Structures, Chris Menzel Re: [ontolog-forum] Universal Basic Semantic Structures, William Frank Re: [ontolog-forum] Universal Basic Semantic Structures, Chris Menzel Re: [ontolog-forum] Universal Basic Semantic Structures, William Frank Re: [ontolog-forum] Universal Basic Semantic Structures, Chris Menzel Re: [ontolog-forum] Universal Basic Semantic Structures, William Frank Re: [ontolog-forum] Universal Basic Semantic Structures, Chris Menzel Re: [ontolog-forum] Universal Basic Semantic Structures, William Frank Re: [ontolog-forum] Universal Basic Semantic Structures, Chris Menzel